Controlling elastic waves with small phononic crystals containing rigid inclusions

¹ Division of Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology (KAUST) - Thuwal 23955-6900, Saudi Arabia
² Key Laboratory of Artificial Micro- and Nano-structures of the Ministry of Education, China and School of Physics and Technology, Wuhan University - Wuhan 430072, China

^(a) ying.wu@kaust.edu.sa

Received: 10 February 2014
Accepted: 29 April 2014

Abstract

We show that a two-dimensional elastic phononic crystal comprising rigid cylinders in a solid matrix possesses a large complete band gap below a cut-off frequency. A mechanical model reveals that the band gap is induced by negative effective mass density, which is affirmed by an effective medium theory based on field averaging. We demonstrate, by two examples, that such elastic phononic crystals can be utilized to design small devices to control low-frequency elastic waves. One example is a waveguide made of a two-layer anisotropic elastic phononic crystal, which can guide and bend elastic waves with wavelengths much larger than the size of the waveguide. The other example is the enhanced elastic transmission of a single-layer elastic phononic crystal loaded with solid inclusions. The effective mass density and reciprocal of the modulus of the single-layer elastic phononic crystal are simultaneously near zero.